4 papers
Hopf substitutions in Species
Aaron Lauve, Anthony Lazzeroni
In the theory of species, the species of linear orders and the substitution operation combine for a compelling result: given any positive comonoid…
Interpolation in Species and a Lift of the Hopf Algebra of r-Quasisymmetric Functions
Aaron Lauve, Anthony Lazzeroni
In this manuscript we lift the theory of r-quasisymmetric functions to the theory of Hopf monoids. We provide a general method of interpolating between two Hopf monoids, one being…
Powersum Bases in Quasisymmetric Functions and Quasisymmetric Functions in Non-commuting Variables
Anthony Lazzeroni
We introduce a new basis for the Hopf algebra of quasisymmetric functions that refine the symmetric powersum basis. Unlike the quasisymmetric power sums of types 1 and 2, our b…
Powersum Bases in Quasisymmetric Functions and Quasisymmetric Functions in Non-commuting Variables
Anthony Lazzeroni
We introduce new bases for the Hopf algebra of quasisymmetric functions that refine the symmetric powersum basis. These bases are expanded in terms of quasisymmetric monomial funct…